… confluence checks based on higher-order critical pairs. A first … termination of all variants of
higher-order rewriting `a la Nipkow, called normal termination, thanks to the notion of a normal …

… complex calculi defined by higher-order rewrite rules such as … to the higher-order case,
yielding the higher-order recursive … A substitution γ is in R-normal form if xγ is in R-normal form …

… This thesis is devoted to the study of termination in higher-order term rewriting. Termination
… The ⇒β relation is terminating on all typed terms and has unique normal forms; that is, if s ⇒…

… characterisation of termination for TRSs to one for HRSs. The definition of Higher-order
Rewriting … To ensure that C really depends on •, the condition that C is in/3-normal form is added. …

… for combining termination and non-termination techniques for first- and higher-order functions
… We implemented and evaluated our results in the automated termination prover AProVE . …

… higherorder rewriting, that is, rewriting higher-order functional expressions at highertypes.
Higher-order … Let R = {Γi ⊣ li → ri}i∈I be a normal higherorder rewrite system such that li ≻β ri …

… We will rely on the fact that canonical (ie long βη-normal) forms of LF object are computable
and that equivalent LF objects have the same canonical form up to α-conversion. We …

… for termination … termination analysis, we apply existing abstract interpretation techniques
directly to the operational semantics, avoiding the need for custom abstractions for termination. …

… to support the use of higher-order datatypes and model concisely … reduction and termination
checking for higher-order logic … We can implement an algorithm for negation normal form …

… existence of a normal form is a weaker property called weak normalization. Termination is
an … A way to prove the termination of this system is to show that, in two successive functions …